Hi Claudine,  A sound post is not at all unusual in a disc music box.
I recently restored an 18" Mira that had a rather large wooden 'bridge'
across the center of the box (front to back).  It was glued to the
soundboard and attached to the back of the bedplate with two really
large screws.  And our Mira has two posts.  Each has a threaded section
which you unscrew to elongate the post and apply tension between the
bedplate and the bottom of the case.

Reginas and other boxes can have something as simple as a one-inch
square block of wood that is a tight fit between the bedplate and the
bottom or back of the case.  A 27" Regina changer has a piece of wood
about 3/4" by 4 inches that is screwed to the back of the bedplate and
connected to the back of the case with a rather large brass clamp (so
you can open the back).

Send me a picture of the part you have and perhaps I can point you to
a good solution.

Regards,
Craig Smith